Grey fleet is usually invisible: no booking, no trip history, no maintenance assurance, often just a mileage claim after the fact. The problem is that work health and safety duty follows the work, not the vehicle's owner, so an employee hurt driving their own car on business is still your incident.
Managing it means knowing when private vehicles are used for work and setting minimum standards. See how IntelliTrac handles employee-owned vehicles.
General information, not tax or legal advice.